If neurons are only defined for values between 0 and 1, how does ReLU differ from the identity?
You are right about the fact that we use nonlinearity for classes that cant be seperated by a straight line. If you think about curves,as we know from the calculus, you can approximate a nonlinear function with lines. If you have infinite amount of lines you can mimic exactly the same function. When you increase or decrease the weight of some neuron you essentially increase or decrease the length of the line it represents. And ReLU solves the vanishing gradient problem so they are superior to sigmoid in my opinion too.